Ken Hanna moved to reassure shareholders at the company's annual general meeting that an international search has begun.
Mr Soames tendered his resignation earlier this year and joins outsourcing company Serco on May 1.
Mr Hanna said: "We, that is the non-executives, have a nomination committee and have been meeting frequently.
"We have employed an international search agency of head hunters and we are considering external as well as internal candidates.
"We are working through a process quickly but we are not going to rush. We want to make sure we get the right person."
Mr Hanna, who became chairman two years ago, admitted he always knew it was likely it would fall to him to find a replacement for Mr Soames, who is one of the longest serving chief executives in the FTSE100.
Then Mr Hanna went to highlight the strength of Aggreko's remaining management team.
He also pointed out the reorganisation of its structure 18 months ago was helping to broaden the experience of executives.
He said: "The board and I feel we are in very safe hands. We have a good strong team."
Mr Soames, who has been with Aggreko since July 2003, received congratulations from shareholders and board colleagues during the course of the meeting at the Grand Central Hotel in Glasgow.
He thanked shareholders and said he always felt the AGM reminded executives of who they were working for.
He said: "Please do not underestimate how important it is that (shareholders) turn up to hold the account the management."
Mr Hanna described Mr Soames as an "outstanding leader" whose contribution to the company had been "immense".
Angus Cockburn, the long serving chief financial officer who becomes interim chief executive, said he would miss Mr Soames and added: "He is an inspirational leader, a great colleague and a friend."
Shareholders formally passed plans for the company to return £200 million of cash to them.
However the board were quizzed over whether that use of funds would leave them less able to make acquisitions.
Mr Hanna said: "We still have good firepower to make the right acquisition. We are not prejudicing our ability to make the right strategic move (by returning money to shareholders)."
Mr Soames described his final full-year in charge as being "creditable in a challenging year".
David Taylor-Smith, Aggreko's regional director for Europe, Middle East and Africa, was asked about growth prospects in Africa and said a recent strategy review pointed to "exciting" potential in the coming years.
All resolutions at the AGM were passed with near unanimous support including the company's remuneration policy, which is now fixed for the next three years, and 2013 remuneration report.
A resolution to increase the maximum amount Aggreko can pay its non-executive directors from £750,000 to £900,000 was also passed with near 99% support.
David Hamill formally stepped down from being the board's senior independent director and that role is being taken up by Russell King.
Ian Marchant, the former SSE chief executive, was also formally approved onto the board having joined last year.
Shares in Aggreko closed up 20p, or 1.3%, at 1559p.